Brackets

Consider all valid bracket sequences of length (2N). These sequences are arranged in lexicographical order, where an opening bracket is considered smaller than a closing bracket. Each sequence is numbered starting from (1).

Your task is to determine the (K)-th sequence in this order.

Input

The first line contains the integer (N) ((1 $\le$ N $\le$ 100)), and the second line contains a natural number (K) ((1 $\le$ K $\le$ 10^1000+255)), which indicates the sequence number you need to find.

Output

Output a single line containing the (K)-th valid bracket sequence of length (2N). The output should not include any spaces. If there are fewer than (K) sequences of length (2N), print "No solution for this testcase." (without quotes).

Examples